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M08.L02 — The Prisoners' Dilemma and Nash Equilibrium

Module: Module 08 — Game Theory and Oligopoly Lesson: L02 of 05 Duration: ~30 minutes Level: Introductory Provenance: OpenStax Principles of Microeconomics 3e | Khan Academy Microeconomics

Learning Objective

Explain why rational individuals might not cooperate, even when it benefits everyone.

The Prisoners' Dilemma Setup

Two suspects (A and B) are arrested. Prosecutors lack evidence for a major charge but can convict on a minor charge (1 year). Each prisoner is offered: - Betray (Defect): Go free if the other stays silent; serve 3 years if both betray. - Stay Silent (Cooperate): Serve 1 year if the other betrays; serve 2 years if both stay silent.

Payoff matrix (years in prison, lower is better):

B: Betray B: Silent
A: Betray -3, -3 0, -3
A: Silent -3, 0 -2, -2

Nash Equilibrium

A Nash Equilibrium occurs when no player can improve their outcome by unilaterally changing strategy. In the Prisoners' Dilemma, the Nash Equilibrium is (Betray, Betray) even though (Silent, Silent) is better collectively.

Worked Example: ACCC and Cartels

Scenario: Two rival firms secretly agree to fix prices (cartel). 1. Payoffs: - If both comply, high profits. - If one defects (lower prices), they gain market share. - If both defect, profits plummet. 2. Incentive: Defect to undercut the rival (dominant strategy). 3. Outcome: Cartels collapse without enforcement (ACCC penalties).

Common Misconception

"Nash Equilibrium always leads to the best group outcome."

The Prisoners' Dilemma shows that Nash Equilibrium can be suboptimal due to individual incentives.

Key Takeaways

  • The Prisoners' Dilemma models conflict between individual and group rationality.
  • Nash Equilibrium describes stable (but not always optimal) outcomes.
  • Cartels are unstable because firms have incentives to cheat.
  • The ACCC enforces anti-collusion laws to protect consumers.

Practice

  1. Why does the Nash Equilibrium in the Prisoners' Dilemma involve both betraying?
  2. How might repeated interactions change firms' incentives?
  3. Explain why the ACCC offers leniency to whistleblowers.

Further Resources

Provenance: OpenStax Principles of Microeconomics 3e | Khan Academy Microeconomics